Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms
Algebraic Geometry
2019-04-03 v2
Abstract
In this work we compute the Dixmier invariants and bitangents of the plane quartics with 3,6 or 9-cyclic automorphisms, we find that a quartic curve with 6-cyclic automorphism will have 3 horizontal bitangents which form an asysgetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equation of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6-cyclic automorphism.
Keywords
Cite
@article{arxiv.1902.02914,
title = {Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms},
author = {Dun Liang},
journal= {arXiv preprint arXiv:1902.02914},
year = {2019}
}
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17 pages